## Bingo! An Ri Masterclasses teaser

This puzzle was devised as part of a Primary Mathematics Masterclass series, and solved by a 9 year-old. Can you crack it?

• Can you solve it?

Last month, the Sunday Times teaser (paywall) was set by Mike Fletcher, a volunteer speaking at one of the hundreds of Ri Masterclass sessions that happen around the country each week, giving some of the country's most enthusiastic children a chance to stretch their brains beyond the curriculum. He first asked this question in a session for primary-aged children, to present a counter-intuitive problem that would spark an interesting thought process in the students. Can you solve it?

The infant teacher played a bingo game with his class. He had two identical dice, the numbers on the six faces of each being 1, 2, 2, 3, 3 and 3.  He told the class that he would throw the pair of dice, add up the two numbers showing, and call that number out in a game of bingo. He then asked each member of the class to make their own bingo card consisting of five numbers of their own choice. He explained that they could repeat a number on their card if they wished (and then delete just one occurrence of the number whenever it was called). Most of the class chose the five possible different totals as their bingo numbers, but one very clever girl chose the best possible selection.

What were her five numbers?

Here’s Mike’s explanation of why he asked the question in his session:

I wanted an interactive probability game to play with children. I wanted the game to reward good play i.e. a child who chose the best bingo card had a good chance of winning. I know from experience a lot of children (and adults, as evidenced by the response to the Sunday Times teaser!) choose all five numbers the same and choose the number that is most likely. In this case a lot of children opt for  5 5 5 5 5  and the rest tend to opt for 2 3 4 5 6. Essentially I wanted a game where I could ask the winner 'Why did you choose those numbers?' and elicit an interesting response from the child that the rest of the group would find enlightening. The teaser printed by the Sunday Times was true except for the fact that the child in question was 9 years old.

Do you know the answer? Sunday Times Teaser enthusiasts have puzzled out the details here and here, or if you just want to know the correct answer, select the hidden text beneath this sentence:

4 4 5 5 6

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